Deformation Theory of the Trivial mod p Galois Representation for GLn

We study the rigid generic fiber $\mathcal{X}^\square _{\overline \rho }$ of the framed deformation space of the trivial representation $\overline \rho : G_K \to \textrm{GL}_n(k)$ where $k$ is a finite field of characteristic $p>0$ and $G_K$ is the absolute Galois group of a finite extension $K/\...

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Bibliographic Details
Published in:International mathematics research notices 2020-11
Main Author: Iyengar, Ashwin
Format: Article
Language:English
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Summary:We study the rigid generic fiber $\mathcal{X}^\square _{\overline \rho }$ of the framed deformation space of the trivial representation $\overline \rho : G_K \to \textrm{GL}_n(k)$ where $k$ is a finite field of characteristic $p>0$ and $G_K$ is the absolute Galois group of a finite extension $K/\textbf{Q}_p$. Under some mild conditions on $K$ we prove that $\mathcal{X}^\square _{\overline \rho }$ is normal. When $p> n$ we describe its irreducible components and show Zariski density of its crystalline points.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnaa011